Traditionally Euler's method, in which the displacement and the velocity at the next time point are calculated by using an initial displacement, initial velocity, and initial acceleration in an interval, has been widely used for the numerical analysis using ordinary differential equation (see patent documents 1 and 2).
Patent document 1: Publication of unexamined patent No. 2004-062676
Patent document 2: Publication of unexamined patent No. 2002-258933